I usually use a crochet hook or a knitting machine seed stitch hook which has a hooks on each ends. Many times when I made mistakes and had to rip a few columns off and then I reknit with my knitting needle. It is easier to see how to do it rather than me explaining. So I've collected a few resources for you to check them out below.
I found these videos and information to be very helpful describing how to pick up a drop stitch using different methods. Please take a minute to watch them and I hope they will help you.
Good luck with your project and thank you for sending in the question.